SUMMARY

This memo is an addendum to OGIP Calibration Memo
CAL/ROS/92-001
(Hasinger et al 1992) in which
we compare the ROSAT PSPC on-axis point spread function psf with
the best signal-to-noise data obtained to date for a point source.
We confirm that the parameterization detailed in
CAL/ROS/92-001 does satisfactorily describe the observed psf
at energies > 0.19 keV.

LOG OF SIGNIFICANT CHANGES

As detailed in CAL/ROS/92-001, the psf of the ROSAT
X-ray mirror assembly (XMA) + PSPC is a convolution of 5 components, 3
of which (namely the XMA scattering profile, the intrinsic spatial resolution
of the PSPC, and Focus and detector penetration effects)
have been parameterized for on-axis observations from PANTER ground
calibration measurements. In CAL/ROS/92-001 it was shown that the
derived analytical functions satisfactorily described
5 moderate signal-to-noise datasets out to a radius ~ 1-2 arcmin
in all but the softest band (B-band; where `Ghost imaging' was already
known to be a problem).
Here we use a very high signal-to-noise (\mathrel\copy6 ×106
photons) dataset of a (nominal)
point source for a detailed comparison of the model psf and
data out to a radius ~ 10 arcmin.

The data used here is proprietary data (PI Thomas) thus the source is
not named here, nor is the observation described in detail. Radial
profiles were extracted centered on the source, using the same method
described in CAL/ROS/92-001, with 5 arcsecond incremental radii, in the
bandpasses as listed in Table 1 of CAL/ROS/92-001.
The lowest 11 PI channels were rejected to exclude
problems due to the variable lower limit discriminator for valid events,
due to the variable instrument gain which is folded into these data.
Any additional sources falling within the specified annuli were masked
out of the analysis.
No background subtraction was carried out. Background rates were
measured from the images and were later folded into the predicted profile
template for each band.

As the in-flight data are affected by more uncertainties than the ground
data (aspect corrections, background subtraction, gain correction etc) it
was not possible to allow profile fitting with the parameters of the
gaussian + exponential + lorentzian components to be free. Instead we
calculated the psf for the source in each bandpass.

First, a spectrum was extracted for the source, in a circle of size
200 arcseconds radius (masking out a nearby source).
Next, a psf was calculated for each energy channel using the
algorithm and parameters given in CAL/ROS/92-0011.
A predicted psf
template was calculated in each band using the source
spectrum to determine the photon weighting to be applied to the psf
component in each energy channel. Thus for each band and spectrum a
combined psf was produced, including a constant term for the
background.

These predicted psf
templates are overlaid on the appropriate datasets in Figure 1.
We stress that the normalization of the model psf in each case
was also calculated using the equations in CAL/ROS/92-001, thus
NO FITTING was performed.
The normalization of the predicted psf was calculated such that the
integral under the predicted template is equal to the integral under
the observed psf.
Discrepancies between the shape of the two curves thus
result in the slight discrepancy at the peak seen in some panels of
Figure 1.

It can be seen that even at this high signal-to-noise ratio,
the psf model provides a good parameterization of the
source profile for all but the B-band. The individual panels give an estimate
of the error in the psf, which it was not possible to illustrate
with lower signal-to-noise data.

C-band (0.188-0.284 keV; panel b)
illustrates a slight excess in
the data at radii ~ 1-2 arcmin,
and a very small excess in the data at radii ~ 3-4 arcmin. Previously
it was thought that the ghost imaging effect was only importnat below
PI channel 15 (0.15 keV), but recent analysis of other high signal-to-noise
data has suggested ghost imaging may be significant up to
channel ~ 30 and thus may significantly affect the
C-band (Nousek & Harnden, p.comm).

These small scale discrepancies may reflect some
of the differences between the ground calibration and in-flight data:

the Gaussian component (due to spatial resolution of the
detector): the width in the model could be narrower than
the data due to residual errors in the attitude corrections.

the exponential component (due to combined focus and penetration
effects): the geometry of the beam used in the
PANTER calibration facility was different to the parallel beam
of the in-flight data. Therefore the detailed shape of the
penetration term could be slightly different in-flight.

the Lorentzian component (due to the scattering profile of the
XRT mirrors): the average grazing angle is slightly larger in the
finite beam than in orbit. Approximately 40% less
mirror scattering is expected in-orbit than on the ground.
In addition, the mirrors may have suffered dust contamination after
the PANTER tests, and may therefore have a greater microroughness
in-flight.

Although there has been no evidence to date to suggest an extended
X-ray component in this source, we note that the signal-to-noise and
spatial resolution obtained here are far superior to any previous
observations of this source (or different source of the same class).
Thus we cannot rule out the possibility that some of the above
discrepancies are due to a contribution of a genuine extended
component associated with the source.

The conclusions given in CAL/ROS/92-001 still hold, and these data give the
best estimate to date of the residual error in the psf model.

Work continues to refine and improve this model, and to extend
this work to include off-axis angles.

ACKNOWLEDGMENTS

We thank the PI. Thomas (MPE), for allowing his proprietary data to
be used in this way, and the many people at MPE involved in the determination
& interpretation of the PANTER data.
We also thank Dave Davis (GSFC) for his help extracting the data.

USEFUL LINKS TO OTHER HTML PAGES

The following useful links are available (in the HTML version of this
document only):

REFERENCES

FIGURE CAPTIONS

Figure 1.
A comparison between the observed and calculated on-axis psf for the
ROSAT PSPC in the 5 energy bands defined in CAL/ROS/92-001.

Footnotes:

1 Note that due to
a typographical error there was a factor 2 missing from eqn 8 of
all versions of CAL/ROS/92-001 prior to 1992 Oct 05 (the
software used to generate the predicted psf and figures was
however correct)